Distributed autonomous systems: resource management, planning, and control algorithms

Transcription

1 Distibuted autonomous systems: esouce management, planning, and contol algoithms James F. Smith III, ThanhVu H. Nguyen Naval Reseach Laboatoy, Code 5741, Washington, D.C., ABSTRACT Distibuted autonomous systems, i.e., systems that have sepaated distibuted components, each of which, exhibit some degee of autonomy ae inceasingly poviding solutions to naval and othe DoD poblems. Recently developed contol, planning and esouce allocation algoithms fo two types of distibuted autonomous systems will be discussed. The fist distibuted autonomous system (DAS) to be discussed consists of a collection of unmanned aeial vehicles (UAVs) that ae unde fuzzy logic contol. The UAVs fly and conduct meteoological sampling in a coodinated fashion detemined by thei fuzzy logic contolles to detemine the atmospheic index of efaction. Once in flight no human intevention is equied. A fuzzy planning algoithm detemines the optimal tajectoy, sampling ate and patten fo the UAVs and an intefeomete platfom while taking into account isk, eliability, pioity fo sampling in cetain egions, fuel limitations, mission cost, and elated uncetainties. The eal-time fuzzy contol algoithm unning on each UAV will give the UAV limited autonomy allowing it to change couse immediately without consulting with any commande, equest othe UAVs to help it, alte its sampling patten and ate when obseving inteesting phenomena, o to teminate the mission and etun to base. The algoithms developed will be compaed to a esouce manage (RM) developed fo anothe DAS poblem elated to electonic attack (EA). This RM is based on fuzzy logic and optimized by evolutionay algoithms. It allows a goup of dissimila platfoms to use EA esouces distibuted thoughout the goup. Fo both DAS types significant theoetical and simulation esults will be pesented. Keywods: fuzzy logic, esouce management, evolutionay computing, obotic contol, distibuted autonomous systems 1. INTRODUCTION A DAS is a collection of machines, such that many of them have an algoithm onboad that allows them to make decisions, adapt to changing conditions in eal-time, and coopeate though communications with the othe machines making up the DAS to incease the pobability of mission success fo the goup. Although not necessaily pat of the definition of a DAS, it is desiable that the decision algoithms allow each machine to execise judgment at the quality level of the best human expets, but much faste. Also, the decision algoithms should make optimal use of the many sensos and othe esouces distibuted ove the DAS. The machines should wok togethe in an optimal fashion. The machines should be able to take into account many diffeent constaints in making thei decisions. Finally, only pocessed infomation should be sent between machines to educe communications bandwidth equiements. Two DASs will be consideed. Pimay attention will be given to a DAS that facilitates localization of an electomagnetic souce (EMS) using matched field pocessing 1,2 (MFP). This DAS, efeed to as the EMS DAS, consists of multiple UAVs each unde the contol of its own decision theoetic algoithm (DTA), an intefeomete platfom (IP) also unde the contol of a DTA and guide stas. The IP is actually an aiplane with an intefeomete onboad that measues emissions fom the electomagnetic souce whose position is to be estimated. The UAVs will measue the index of efaction of the atmosphee in eal-time to facilitate estimation of the EMS position though matched field pocessing. In MFP, measued field emissions fom a souce whose position is unknown ae compaed to theoetically calculated electomagnetic fields, efeed to as eplica fields. To calculate the eplica fields the index of Coespondence: jfsmith@dsews.nl.navy.mil Signal Pocessing, Senso Fusion, and Taget Recognition XIV, edited by Ivan Kada, Poc. of SPIE Vol (SPIE, Bellingham, WA, 2005) X/05/$15 doi: /

2 efaction of the popagation medium is essential, thus the eason fo the UAV measuements. The guide stas ae objects of known position, magnitude and phase that have been placed in position by the blue foce. The blue foce is the goup desiing to know the position of the EMS. The guide stas popeties ae used to coect fo wavefont distotion (WFD) in a fashion simila to WFD coection methods in astophysics and ultasonics 3,4. The DTA aboad the UAVs will allow them to detemine thei own couse, change couse to avoid dange, sample phenomena of inteest that wee not pe-planned, and coopeate with othe UAVs and othe machines in the DAS. The second DAS poblem to be consideed is multi-platfom coopeative electonic attack (MEA). The MEA DTA was evolved fo it by a symbolic evolutionay algoithm 5 (SEA). The MEA algoithm assumes data has aleady been fused, including IDs. This DTA allows a goup of platfoms to automatically engage in coopeative electonic attack (EA). They will automatically help each othe, and combine EA techniques and powe fo geate success. Also, the goup emains stable if platfoms ae lost, and late aiving platfoms may join the DAS without hesitation and contibute to its success. This DTA does not equie human intevention. Thee is no human commande cental o local. To be consistent with teminology used in atificial intelligence and complexity theoy 6, the tem agent will sometimes be used to mean platfom, also a goup of allied platfoms will be efeed to as a meta-agent. Finally, the tems blue and ed will efe to agents o meta-agents on opposite sides of a conflict, i.e., the blue side and the ed side. Section 2 povides an oveview of electomagnetic souce localization though MFP using mutiple UAVs fo ealtime index of efaction measuement and motivates the need fo the algoithms descibed in subsequent sections. Section 3 discusses the electomagnetic measuement space, UAV isk, UAV isk toleance and the planning algoithm. Section 4 discusses DAS inteactions and the contol algoithm. Section 5 discusses the MFP based post-pocessing algoithm and validation. Section 6 povides a compaison of DAS inteaction models. Finally, section 7 povides a summay. 2. ELECTROMAGNETIC SOURCE LOCALIZATION THROUGH MFP It is fequently desiable to be able to estimate the position of an electomagnetic souce. One appoach involves the use of hybid time-diffeence-of-aival 7 (TDOA) methods to apidly geo-locate theats based on RF emissions. These techniques equie multiple platfoms with sophisticated senso suites and vey high bandwidth data links to detemine unambiguous geo-location. Anothe appoach that escapes the equiements fo sophisticated sensos and ulta-high bandwidth communications is MFP. In MFP an intefeomete detects the electomagnetic emissions of the EMS. Estimates ae made fo the possible positions of the EMS. Fo each possible position a theoetical electomagnetic field is calculated as if thee wee an EMS at that position. These theoetical fields ae known as eplica fields. The eplica fields ae compaed though an inne poduct with the measued field. The position coesponding to the maximum value of the inne poduct is the EMS s MFP position estimate. The MFP pocedue has been applied extensively in acoustics 1,2 and shows pomise fo electomagnetic souce localization. To calculate the eplica fields essential to the MFP algoithm, it is necessay to known the index of efaction of the atmosphee between the EMS and the IP. The index of efaction is subject to shot time scale fluctuations and ove longe peiods of time can change significantly. In addition, thee can be phenomena that can seiously impact the MFP position estimates. An example is the fomation of a adio hole 8. If the IP should fly into a adio hole then it will not be able to ecod emissions fom the EMS. If some of the elements of the intefeomete should happen to be in the adio hole and othes not, and the adio hole is not modeled in the eplica field calculations, then the MFP position estimation eo can be significant. Fo the easons outlined, it is useful to have eal-time updates of the index of efaction. The function of the EMS DAS will be to conduct eal-time measuements of the index of efaction. Each UAV will have its own DTA allowing it to detemine new optimal tajectoies in eal-time subject to changing conditions. Also, the DTAs on the UAVs will allow them to coopeate to incease the pobability of mission success. Thee will be two diffeent types of coopeation allowed by the DTA and thee classes of help equests which ae discussed in section 4.2. The fist type of coopeation that the UAVs may exhibit is to suppot each othe if thee is evidence that an inteesting physical phenomenon has been discoveed. If one UAV seems to have discoveed a adio hole, it can equest that 66 Poc. of SPIE Vol. 5809

3 anothe UAV o UAVs help detemine the extent of the adio hole so the IP can fly aound it. Simila coopeation can be caied out if a UAV may have discoveed othe elevated extended weathe systems. The second type of coopeation that the UAVs can exhibit though thei DTAs is when a UAV is malfunctioning o may be malfunctioning. If a UAV s intenal diagnostics indicate a possible malfunction, then it will send out an omnidiectional equest to the othe UAVs fo help. Each UAV will calculate its pioity fo poviding suppot using a fuzzy logic pocedue descibed below. The UAVs send thei pioity fo poviding suppot message back to the equesting UAV. The equeste subsequently sends out a message infoming the goup of the ID of the highest pioity UAV. The high pioity UAV then poceeds to aid the equeste. The suppot povided by the helping UAV can take on diffeent foms. If the equeste suspects a malfunction in its sensos, the helpe may measue some of the same points oiginally measued by the UAV in doubt. This will help establish the condition of the equeste s sensos. If additional sampling indicates the equeste is malfunctioning, and epesents a liability to the goup it will etun to base. In this case the suppote may take ove the mission of the equeste. Whethe o not the suppote samples all the emaining sample points of the equeste; subsequently, abandoning its oiginal points depends on the sample points pioities. A fuzzy logic based pocedue fo detemining sample point pioities is discussed below. If it is established that the equeste is not malfunctioning o the equeste can still contibute to the mission s success it may emain in the field to complete its cuent mission. Figue 1 povides an oveview of the pocess. The filled cicle epesents an EMS. The double-aow epesents an intefeomete that will measue emissions fom the EMS. The unfilled tiangles ae UAVs that wok in a coodinated fashion to measue the index of efaction. These index of efaction measuements ae sent to the intefeomete platfom to be incopoated into the eplica field calculations, which is pat of the MFP estimation pocess. The sta shaped objects ae the guide stas. The guide stas ae inexpensive multi-spectal electomagnetic souces of known position, magnitude and phase. Thei positions ae pe-calculated by the planning algoithm allowing them to be deposited in optimal locations. Since they will be beacons of known position, magnitude and phase they can be used to coect fo wavefont distotion (WFD) due to inhomogeneities in the popagation envionment. This ultimately should impove the EMS position estimate. This pocess of WFD coection is kinded to what is done in obsevational astophysics when using a Knox-Thompson algoithm 3. Given a sta of unknown magnitude and phase within a tubulence cell whee thee is a sta of known magnitude and phase, the Knox-Thompson algoithm effectively allows the estimate of the unknown sta s magnitude and phase while subtacting out the effect of the eath s tubulent atmosphee. 3. MEASUREMENT SPACE, RISK, RISK TOLERANCE AND THE PLANNING ALGORITHM The measuement space consists of the electomagnetic popagation envionment whee UAVs and the IP make thei measuements. This envionment includes sampling points and the desiable neighbohoods that suound them. The sampling points o the desiable neighbohoods ae whee the UAVs will make measuements. The method of detemining the sampling points and desiable neighbohoods is descibed below. The measuement space also includes taboo points and the undesiable neighbohoods that suound them. The taboo points ae points of tubulence and othe phenomena that could theaten the UAVs. The undesiable neighbohoods suounding them also epesent vaious degees of isk. The method of specifying taboo points and quantifying the degee of isk associated with thei undesiable neighbohoods employs fuzzy logic and is discussed in subsection Planning algoithm The planning algoithm allows the detemination of the minimum numbe of UAVs needed fo the mission subject to fuel constaints, isk, UAV cost, and impotance of vaious points fo sampling. Risk efes to tubulent egions o egions undesiable fo othe easons, e.g., the pesence of enemy obseves o physical obstuctions. Risk may also be incued if the UAV s populsion o senso systems ae consideed uneliable. The planning algoithm automatically establishes the ode in which to send the UAVs taking into account the UAV s value; onboad senso payload; onboad esouces such as fuel, battey, compute CPU and memoy; etc. The pioity of sampling points and thei desiable Poc. of SPIE Vol

4 neighbohoods ae taken into account. The planning algoithm also calculates the optimal path aound undesiable egions outing the UAVs to o at least nea the points to be sampled. In the planning phase, the location of the EMS is unknown. Some positions ae moe likely than othes fo the EMS s location. When establishing likely positions fo the EMS, human expets ae consulted. The expets povide subjective pobabilities of the EMS being located at a numbe of positions. These likely EMS locations ae efeed as hypothesis positions. Ray-theoetic electomagnetic popagation 8 is conducted fom each hypothesis position to each intefeomete element on the IP. The points on the sampling gid neaest the points of each ay s passage ae the sampling points. The pioity of a sampling point is equal to the subjective pobability of the hypothesis position fom which the associated ay emeges. Each sampling point is suounded by what ae efeed to as desiable neighbohoods. Depending on local weathe, topogaphy, etc., the desiable neighbohoods ae geneally concentic closed balls with a degee of desiability assigned to each ball. The degee of desiability chaacteizes the anticipated vaiation in the index of efaction. If fo that egion of the measuement space, the spatial vaiation of the index of efaction is slow, the degee of desiability may assume its maximum value of unity fo a ball of adius measued in miles. Fo egions of space whee the index of efaction s spatial vaiation is geate, the degee of desiability may fall off much moe apidly, appoaching the minimum value of zeo afte just a mile o two. The desiable egion need not have spheical geomety. Rotational symmety may be boken by a vaiety of pocesses, e.g., an elevated duct, a adio hole, etc. The notion of a desiable neighbohood is motivated by the fact that a sampling point may also be a taboo point o eside within an undesiable neighbohood. In the case the sampling point coincides o is nea a taboo point and at least pat of the sampling point s desiable neighbohood falls within the taboo point s undesiable neighbohood, the UAV may only sample within a desiable neighbohood that is consistent with its isk toleance. 3.2 UAV isk, the fuzzy isk tee and isk toleance A point may be labeled taboo fo a vaiety of easons. A taboo point and the undesiable neighbohoods containing the point geneally epesent a theat to the UAV. The theat may take the fom of high winds, tubulence, icing conditions, mountains, etc. The undesiable neighbohoods aound the taboo point elate to how spatially extensive the theat is. This section uses fuzzy logic to quantify how much isk a given neighbohood poses fo a UAV. This quantitative isk is then incopoated into the UAV s cost fo taveling though the neighbohood as descibed in subsection 3.3. Once the cost is established an optimization algoithm is used to detemine the best path fo the UAV to each its goal subject to isk, isk toleance and many othe issues Quantifying UAV isk and isk toleance When detemining the optimal path fo the UAVs to follow both the planning algoithm and the contol algoithm unning on each UAV takes into account taboo points and the undesiable neighbohood aound each taboo point. The path planning algoithm and contol algoithm will not allow a UAV to pass though a taboo point. Depending on the UAV s isk toleance a UAV may pass though vaious neighbohoods of the taboo point, subsequently expeiencing vaious degees of isk. Both the concepts of isk and isk toleance ae based on human expetise and employ ules each of which cay a degee of uncetainty. This uncetainty is bon of linguistic impecision 9, the inability of human expets to specify a cisp assignment fo isk. Owing to this uncetainty it is vey effective to specify isk and isk toleance in tems of fuzzy logic. Risk is epesented as a fuzzy decision tee 5,10-14 as depicted in Figue 2. The isk subtee defined below is a subtee of the lage isk tee that was actually used. The isk tee is used to define taboo points and the undesiable neighbohoods suounding the taboo points. The oot concepts on the isk tee use the membeship function defined in (1-3), 68 Poc. of SPIE Vol. 5809

5 µ ( x) oot _ concept 1, if = 0 3 4, if 0 < 1 l = 1 2, if 1 l < 2 l 1, if 2 l < 3 l 4 0, if > 3 l = x, q taboo (1) (2) q taboo = position of taboo point. (3) whee taboo point is the point at which the isk phenomenon has been obseved. The oot concepts used on the isk subtee ae given in (4). oot_concept RC={Mountains, High Tension Wies, Buildings, Tees, Smoke Plumes, Suspended Sand, Bids/Insects, Othe UAVs, Ai Polution, Civilian, Own Militay, Allied Militay, Neutal Militay, Cold, Heat, Icing, Rain, Fog, Sleet, Snow, Hail, Ai Pocket, Wind, Wind Shea, Hostile Action/Obsevation} (4) The values taken by the quantity l will be discussed in a futue publication. The fuzzy membeship function fo the composite concept RISK is defined as µ ( x ) RISKt = α RC µ ( x ) α, (5) with the Undesiable Neighbohood defined as follows: ( ) { x µ 4 } x 1 Undesiabl e Neighbohood =. RISK (6) The concept of isk toleance is used to specify the subset of the undesiable neighbohood that a UAV may fly though. The isk toleance, τ i, of the i th UAV, UAV(i) is defined such that UAV(i) may fly though the following subset of the undesiable neighbohood of taboo point, q taboo, ( ) { x 0 < µ i } x τ Risk Toleant Subset =. RISK (7) The concept of isk toleance is defined to allow highe isk settings fo the UAVs. By letting the UAVs have geate isk toleance it is anticipated that the pobability of mission success will be geate. It is also anticipated that the pobability of the mission s cost exceeding a highe theshold will also be highe. The effect of a vaiable isk toleance on the DAS s pobability of mission success and pobability of cost exceeding a cetain theshold will be investigated in detail in the nea futue. Fo now isk toleance is simply a paamete to be set. In the futue it will be endeed as a function of the value of the UAV in dollas, the UAV s populsion system popeties and estimated eliability, the sampling points pioity, etc. Poc. of SPIE Vol

6 3.3 Cost matix The best path algoithm is actually an optimization algoithm that attempts to minimize a cost function to detemine the optimal tajectoy fo each UAV to follow, given a pioi knowledge. The cost function fo the optimization algoithm takes into account vaious factos associated with the UAV s popeties, mission and measuement space. Two significant quantities that contibute to the cost ae the effective distance between the initial and final poposed positions of the UAV and the isk associated with tavel. Fo puposes of detemining the optimal path, the UAV is assumed to follow a ectilinea path consisting of connected lines segments, whee the beginning and ending points of each line segment eside on the UAV s sampling lattice. Let A and B be two gid points on the UAV s sampling gid with coesponding position vectos, A and B, espectively. Denote the effective distance between A and B as d( A,B ). If both A and B ae sample points then the UAV tavels at sampling velocity, othewise it tavels at non-sampling velocity. If both A and B ae sample points then the effective distance is the Euclidean distance between the points multiplied by the atio of the sampling speed to the non-sampling speed; othewise, it is simply the Euclidean distance between the points. If only the effective distance between points A and B and the tavel isk ae taken into account the path cost is given by d(, ) + µ ( ) V( i ), whee V(i ) is defined to be the elative value of the i th UAV in $10,000 units. A B RISK B Two othe concepts contibuting to the path cost ae estimates of the eliability of the i th UAV s sensos and populsion system. Let these eliability estimates be denoted as µ s and µ p, espectively. These fuzzy gades of membeship in the concepts senso eliability and populsion eliability, abbeviated as s and p, espectively, assume values between zeo and one, inclusive. A value of unity implies high eliability; and a value of zeo, that the system is totally uneliable. A fom of the path cost that incopoates Euclidean distance, tavel isk, and eliability is path _ cost( A,B ) d( 1 1 A,B ) + µ RISK( B ) V(i ) + ( + 2 ) V( i ) µ (, ) µ (, ). = s A B p A B (8) If the total candidate path fo the mission consists of the following points on the UAV lattice, Path( i ) K { A, A,, } =, (9) 1 2 A n then the total path cost is defined to be n 1 j= 1 total _ cost( Path( i )) path_cost( A,A. j j+ 1 ) (10) The fom of the path cost given in (8, 10) is non-unique, a vaiety of expessions might be used. The expession on the ight-side of (8) has the advantage that if eithe the sensos o populsion systems ae totally uneliable, the cost goes to infinity, which is appopiate since such an extemely uneliable UAV should not be used. If both sensos and populsion ae extemely eliable, then the contibution to the path cost elated to eliability issues is zeo due to the subtaction of two on the ight-side of (8). Finally, the eliability tems in (8) can be made a function of time o the end points of the line segment being tavesed, this allows the modeling of decaying eliability, automatic epai pocesses o a UAV that automatically switches to a edundant senso system when the pevious senso fails. Detemining the optimal path fo the the i th UAV consists of minimizing (10) such that the total tavel time emains less than the amount of fuel and battey life measued in time. Also, the fuzzy membeship functions coesponding to senso and populsion isk must emain below thei associated thesholds. The planning algoithm detemines the path each UAV will pusue, which points will be sampled, the minimum numbe of UAVs equied fo sampling the points and makes assignments of UAVs fo measuements at paticula points. 70 Poc. of SPIE Vol. 5809

7 UAVs ae assigned as a function of thei abilities to sample high pioity points fist. The planning algoithm assigns as many high pioity points to a UAV as possible with the UAV s fuel, battey life, estimated eliability and effectiveness being the limiting constaints. When the planning algoithm detemines a UAV has been assigned as many points as it can handle, assignments ae made to the next highest pioity UAV. This pocess is continued until the points equied fo sampling ae exhausted. It is impotant to obseve that a single UAV can sample points of diffeent pioity if that is efficient. Finally, if thee ae not enough UAVs to sample all the points, the appoach undelying the planning algoithm assues the highest pioity points ae sampled fist, leaving the lowest pioity sampling point to the last. 4. DAS INTERACTION AND THE CONTROL ALGORITHM The planning algoithm detemines based on the best a pioi knowledge the minimum numbe of UAVs equied fo the measuement pocess, the ode in which UAVs ae used, the paths the UAVs will fly, the pioity of points to be sampled and egions to avoid. Duing the tavel and measuement pocess it is inevitable that pioity of points fo sampling will change, new inteesting physical phenomena will be discoveed and old points will pove to be uninteesting. Also egions, initially thought to be theatening will pove to be benign and it will become moe efficient to eoute UAVs though these peviously excluded egions. Sampling new points, ignoing points that ae no longe of inteest and eouting though new egions equie an algoithm that allows changes in eal-time. This section will descibe the eal-time contol algoithm and the types of inteactions it allows between the UAVs and the IP. 4.1 Oveview of eal-time contol Each UAV has a eal-time algoithm onboad it that allows ecalculation of paths duing flight. As in the case of the planning algoithm the contol algoithm uses an A-sta algoithm 15 to do the best path calculation, employs fuzzy logic and solves a constained optimization poblem. Although this can equie a numbe of minutes of computation on a two to thee gigahetz compute, this is consideed adequate given the equied UAV flight time between points. A ecalculation of flight paths can be tiggeed by a numbe of events such as a weathe boadcast that indicates new taboo egions, the discovey by a UAV of a potential elevated system like a adio hole, malfunctions o suspected malfunctions. All of these conditions can esult in help messages being tansmitted between the UAVs. These help messages can esult in inteactions between the UAVs based on tansmission of the esults of pioity calculations fo endeing suppot to the equesting UAVs. The cuent fomulation of the contol algoithm gives the UAVs significant autonomy in making decisions about tavel, measuement, and endeing suppot to othe UAVs. This appoach is still unde evaluation. 4.2 Methods of assigning pioity fo poviding suppot Cuently in the contol stage, when a UAV discoves an inteesting physical phenomenon, is malfunctioning, o suspects due to intenal eadings that it is malfunctioning, it sends out a equest fo help. Each UAV eceiving this message calculates its pioities fo poviding assistance to the UAV in need. This pioity calculation gives ise to a numbe between zeo and one, inclusive, which is subsequently tansmitted to the oiginal UAV desiing suppot. The equesting UAV sends out an omni-diectional message with the ID of the UAV with highest pioity fo contibuting suppot. The high pioity UAV then flies into the necessay neighbohood of the equesting UAV to povide help The thee equest classes Thee ae thee classes of help equest. The fist occus when a UAV, the equeste, detemines it may have discoveed an inteesting physical phenomenon. This phenomenon may be an elevated duct, adio hole, ain system o some othe type of system with physical extent. The equeste desies to detemine if the phenomenon has significant extent. It will equest that a helping UAV o UAVs sample likely distant points within this phenomenon. The second class of help equest elates to a UAV that accoding to intenal diagnostics may be expeiencing a senso malfunction. This UAV will equests that anothe UAV o UAVs measue some of the points that the equesting UAV measued. This will help detemine if the UAV is actually malfunctioning. If the equesting UAV is detemined to be malfunctioning, then it will fly back to base, if it is capable. The detemination of whethe it is actually malfunctioning Poc. of SPIE Vol

8 equies some consideation. Since the second UAV will pobably be measuing a distant point at a time diffeent than the oiginal equesting UAV made its measuements, potential vaiation in the index of efaction ove time must be taken into account. The thid equest class occus when a UAV has definitely detemined that it is malfunctioning and should not o can not continue to sample. The suppoting UAV will take ove the equeste s sampling task. The equeste etuns to base if possible Detemining the pioity of contibuting suppot The detemination of pioity of contibuting suppot (PCS) cuently uses fuzzy logic and is a weighted sum of fou contibuting tems. These tems ae the value in dollas of the UAV, the distance of the potential helpe fom the position whee help is to be endeed, the amount of fuel the suppoting UAV has, and the pioity of the points the potential suppoting UAV was scheduled to sample. It is likely this weighted sum, if it is to be used in the futue should include othe tems. The new tems would involve the estimated eliability of the helping UAV s sensos and populsion systems, the pioity of the points that the equesting UAV desies to be sampled as well as the pioity of the points othe adjacent UAVs ae sampling. This last pioity elated to adjacent UAVs is intoduced because, if the potential suppote flies a geat distance to help a UAV with elatively low pioity sample points and a UAV that was adjacent fails, then some vey high pioity points may not be sampled. 5. MFP POST-PROCESSING ALGORITHM AND VALIDATION While the UAVs make index of efaction measuements they ae sending this infomation to a base facility o the IP. Once sufficient index of efaction measuements ae eceived and the IP has ecoded sufficient emissions fom the EMS, then MFP post-pocessing can be conducted. The MFP yields an estimate of the location of the EMS, which is the ultimate goal of the coopeative measuement behavio of the IP and the UAVs. In a simulation envionment whee tuth is known the MFP step can be used to show the effectiveness of the entie pocess. This section discusses the thee main MFP pocessos used including techniques that take advantage of the fact that the IP is a moving platfom. The section concludes with a discussion of MFP esults. 5.1 MFP pocessos Many MFP pocessos have been applied in the undesea acoustics liteatue 1. Fo this initial electomagnetic effot thee pocessos wee applied: the simple linea pocesso, the gadient pocesso and the extended linea pocesso. As peviously noted, MFP compaes the EMS emission measuements made by an intefeomete. The intefeomete used will typically have multiple elements. Each element will be used to make a measuement. The measued values ae used to fom a vecto efeed to as the measuement vecto (MV). Fom vaious hypothesis positions eplica fields ae calculated and the esults of measuement by each intefeomete element ae simulated. The simulated measuements ae used to fom a vecto analogous to the one fomed fom the measuement pocess and efeed to as a eplica vecto (RV). Thee is a RV calculated fo each eplica field The simple linea MFP pocesso Fo the case of the simple linea MFP pocesso (SLMP) measuement and eplica vectos ae detemined at only one position of the IP. The use of the wod simple in the designation simple linea MFP pocesso efes to fomation of the vectos afte making measuements at only one position of the IP. Both the measuement vecto and the eplica vectos ae endeed as unit vectos by dividing by thei espective noms. The esulting unit vectos ae efeed to as the unit measuement vecto (UMV) and unit eplica vecto (URV), espectively. The SLMP is the inne poduct of the UMV and the URV. Fo the SLMP, the best position estimate coesponds to the hypothesis position that maximizes the SLMP. 72 Poc. of SPIE Vol. 5809

9 5.1.2 The gadient MFP pocesso and IP motion The IP is a moving platfom and ove time the EMS will make multiple emissions. The gadient MFP pocesso (GMP) takes advantage of the motion of the IP and multiple emissions in time of the EMS. Fo the GMP, the diffeence between MVs at two IP positions is ecoded. Fo a single position of the IP, the diffeence in measued values acoss the intefeomete elements is also ecoded. The two types of diffeences allow patial deivatives and hence the field gadient to be appoximated as atios of finite diffeences. The MV vecto is eplaced by a measuement matix (MM) whose enties coespond to the gadient of the measued electomagnetic field. An analogous eplica MFP matix (RMM) is calculated fo each eplica field. Both the MM and the RMM ae nomalized by dividing by the squae oot of the sum of the squaes of each matix s espective elements. This nomalization pocedue is caied out so that when a sum of squaes of each nomalized matix s elements is computed, the esult is unity fo non-zeo matices. These nomalized matices ae efeed to as the unit MM (UMM) and unit RMM (URMM), espectively. The GMP consists of foming the sum of the poduct of coesponding elements of the UMM and URMM. The best GMP position estimate aises fom the hypothesis position that maximizes the GMP The extended linea aay MFP pocesso and IP motion The extended linea aay MFP pocesso (ELAMP) also takes advantage of the IP s motion. Instead of esticting measuements to two IP positions, the ELAMP can incopoate measuements at many positions, typically fou. Fo the ELAMP, the MV consists of concatenations of the MVs fo each position. The UMV is fomed by dividing by the concatenated vecto s nom. The URV is fomed in an analogous fashion fo each eplica field calculation. The ELAMP is the inne poduct between the UMV and the URV. The hypothesis position that maximizes the ELAMP coesponds to the best MFP position estimate. 5.2 MFP esults Computational expeiments wee conducted using a vaiety of meteoological conditions and all thee pocessos. Guide sta based WFD coection was not incopoated, but will be included in futue publications. The simulated EMS was assumed to have a fequency of one gigahetz. It is well known that at such high fequencies thee can be significant fluctuations in the EMS field due to small inhomogeneities in the popagation envionment. These fluctuations can have a significant effect on the SLMP, esulting in a eduction of EMS position estimate quality. Fo an EMS and IP sepaated by 50 miles in a popagation envionment with a vetically statified index of efaction field, small andom azimuthal vaiations in the index of efaction could poduce an estimation eo of the EMS position of a mile o moe even afte coection of the index efaction using UAV measuements and an index of efaction intepolation model. Due to the use of measuements at two diffeent positions, the GMP was able to poduce bette MFP position estimates. The eo in position estimate afte using measued index values and intepolation was typically well unde one mile. In some expeiments, pesumably due to the inclusion of additional measuements made by the IP, the ELAMP showed esults supeio to the SLMP and the GMP. Afte eplacing the oiginal index of efaction field with one constucted fom UAV measuements that wee subsequently intepolated, the ELAMP yielded position estimates with an eo typically on the ode of feet o less. All thee pocessos exhibited eos in position estimates of a mile o moe ove 50 miles if exteme hoizontal vaiation in the index of efaction was pemitted. An initial examination of expeimental data and consultation with expets seems to show that such exteme hoizontal vaiation in index of efaction ove the space of one to five miles is not obseved in natue most of the time so this is not consideed a significant difficulty with the MFP pocedue. Fo all thee MFP pocessos thee wee fluctuations in pefomance that must be exploed and explained. Notably, when some intefeomete elements wee tuned off, esulting in a smalle numbe of measuements, the MFP estimate impoved. Pesumably, this elates to the model of the index of efaction allowing andom hoizontal vaiation in value. If fo a paticula element the andom vaiation was lage and this was not modeled in the eplica field then a paticula intefeomete element could bias the MFP estimate. Fotunately, as obseved above this type of phenomenon seems to be ae in natue. Poc. of SPIE Vol

10 6. COMPARISON OF DAS INTERACTION MODELS It is inteesting to compae the EMS DAS to the peviously efeenced MEA DAS. The MEA DAS has been unde development longe than the EMS DAS. Both DAS allow inteaction between the agents making up the DAS. In some vesions of the MEA DAS, like the EMS DAS help equest ae adiated in an omni-diectional fashion with potential suppotes each sending a pioity scoe to the equeste. The equeste then sends a confimation to the agent with highest pioity that it may help. The MEA DAS shows geate flexibility in behavio by vitue of it fuzzy paamete selecto tee (FPST), a fuzzy decision tee that allows the MEA RM to change its paametes and hence behavio significantly in eal-time. A FPST has not been intoduced into the EMS DAS contolle as of yet. This will be a subject of futue consideation. The MEA DAS also shows diffeence foms of coopeation between agents since fo diffeent theats the RM can select diffeent combined electonic attack (EA) techniques. This eflects the diffeent poblem that motivated the MEA DAS s design. It is likely the diffeent types of inteactions that the UAVs ae subject to, fo the EMS DAS will incease in futue vesions. 7. SUMMARY A distibuted autonomous system (DAS) consists of a collection of machines o agents, most of which have some autonomous decision making ability that allows them to inteact though communication fo the mutual benefit of the DAS. A DAS consisting of a collection of unmanned aeial vehicles (UAVs), an intefeomete platfom (IP) and guide stas has been discussed as well as thee elated algoithms that ae unde development. The IP measues emissions fom an electomagnetic souce (EMS) and the UAVs measue the index of efaction of the popagation envionment in ealtime. The emissions and index of efaction measuements ae used in a pocess known as matched field pocessing (MFP) to estimate the position of the EMS. Thee algoithms ae discussed that facilitate the MFP pocess. The fist is the planning algoithm that detemines which points to sample and which UAV will sample them, the path that each UAV and IP will fly, and the position of the guide stas. The second algoithm is the contol algoithm. This algoithm esides on each UAV and allows it to changes its path, sampling points and coopeative behavio with espect to the IP and othe UAVs in eal-time. Both the planning algoithm and contol algoithm employ best path algoithms, fuzzy logic and constained optimization. The final algoithm discussed is the post-pocessing algoithm that incopoates the measued quantities into a MFP estimate of the EMS position. Expeimental and validation esults ae discussed. Compaisons ae dawn between the EMS DAS contol algoithm and a esouce manage developed peviously fo a DAS dedicated to multiple platfom coopeative electonic attack. ACKNOWLEDGEMENTS This wok was sponsoed by the Office of Naval Reseach. The authos would also like to acknowledge M. Alan Schultz, D. Lawence Schuette, D. Jeffey Heye, D. Fancis Klem, D. Gegoy Cowat, and D. Peston Gounds. REFERENCES 1. A. Tolstoy, Matched Field Pocessing fo Undewate Acoustics, Chapte 2, Wold Scientific, Singapoe, J.F. Smith, III, O. Diachok, R. Heitmeye, and E. Livingston, ``Low Fequency Bathymetic Effects on Long-Range MFP Signal Pefomance in the Notheast-Pacific, Full Field Invesion Methods in Ocean and Seismic Acoustics, O. Diachok, A. Caiti, P. Gestoft, H. Schmidt, Kluwe Academic Publishes, Boston, G.R. Ayes, M.J. Nothcott, and J.C. Dainty, Knox-Thompson and Tiple-Coelation Imaging Though Atmospheic Tubulence, Jounal of the Acoustical Society of Ameica, A, 5(7), pp , R.C. Waag, J.F. Smith III, and Y. Sumino, ``Wavefont Distotion in Ultasonic Imaging, IEEE EMBS 11th Int. Confeence Poceedings, Institute of Electical and Electonics Enginees, Seattle, James F. Smith, III, Fuzzy logic esouce manage: eal-time adaptation and self oganization, Signal Pocessing, Senso Fusion, and Taget Recognition XIII, I. Kada, Vol. 5429, pp , SPIE Poceedings, Olando, Poc. of SPIE Vol. 5809

11 6. J. H. Holland, Hidden Ode How Adaptation Builds Complexity, pp. 1-15, Peseus Books, Reading, D. C. Schlehe, Electonic Wafae in the Infomation Age, Chapte 1, Atech House, Boston, L.V. Blake, Rada Range-Pefomance Analysis, Atech House, Boston, L.H. Tsoukalas and R.E. Uhig, Fuzzy and Neual Appoaches in Engineeing, Chapte 5, John Wiley and Sons, New Yok, S. Blackman and R. Popoli, Design and Analysis of Moden Tacking Systems, Chapte 11, Atech House, Boston, James F. Smith, III, Fuzzy logic esouce manage: decision tee topology, combined admissible egions and the self-mophing popety, Signal Pocessing, Senso Fusion, and Taget Recognition XII, I. Kada, Vol. 5096, pp , SPIE Poceedings, Olando, James F. Smith, III, Co-evolutionay Data Mining to Discove Rules fo Fuzzy Resouce Management, Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, H. Yin, pp , Spinge-Velag, Mancheste, J.F. Smith III; Genetic Pogam Based Data Mining fo Fuzzy Decision Tees, Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, Z.R. Yang, R. Eveson, H. Yin, pp , Spinge-Velag, Exete, James F. Smith, III, Data Mining fo Fuzzy Decision Tee Stuctue with a Genetic Pogam, Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, H. Yin, N. Allinson, R. Feeman, J. Keane, S. Hubbad, pp , Spinge-Velag, Mancheste, S.J. Russel and P. Novig, Atificial Intelligence: A Moden Appoach (2nd Edition), Pentice-Hall, Englewood Cliffs, EMS Intefeomete Figue 1: The gid epesents the electomagnetic popagation envionment; the filled cicle, the EMS whose position is to estimated, the double-headed aow, the IP platfom; unfilled tiangles, UAVs; and the sta shapes, guide stas. Poc. of SPIE Vol

12 Risk Bids/Insects Taffic Weathe Hostile Action/ Obsevation Tubulence Othe UAVs Civilian Own Militay Neutal Militay Allied Militay Tempeatue Wind Wind- Shea Cold Heat Ai Pocket Icing Pecipitation Hail Suspended Systems & Rain Snow Contaminants Fog Sleet Ai- Pollution Smoke Physical Plumes Obstuctions Mountains Tees Suspended Sand Buildings High Tension Wies Figue 2: The fuzzy isk tee and its 25 fuzzy oot concepts. 76 Poc. of SPIE Vol. 5809